Local oscillator frequency offset (LOFO) is a frequency offset between a received data carrier and a local oscillator. For lasers used in coherent optical communication systems, a LOFO can reach up to about +/−3 gigahertz (GHz) and can create a linear ramp in the phase of mixed signals. Some existing solutions are limited to single carrier applications. Other existing solutions estimate and compensate LOFO in a carrier recovery block by accumulating successive symbol phase errors. Alternatively, after chromatic dispersion compensation, LOFO is estimated from phase errors of a series of adjacent training symbols.
However, existing solutions are not suitable for spectral-shaping subcarrier modulation (SS-SM) because chromatic dispersion compensation cannot be performed before LOFO compensation. In an SS-SM receiver, a frequency domain equalizer (FDEQ) performs a frequency domain demultiplexing function to separate subcarriers for chromatic dispersion compensation. Chromatic dispersion refers to the condition where the group velocity of light in a medium (e.g., a fiber) varies with optical frequency. When chromatic dispersion is present, different frequency contents of a signal will arrive at different times at a receiver, and this causes signal distortion. Frequency domain demultiplexing requires prior knowledge of LOFO values for proper separation of subcarriers in the frequency domain. To avoid data degradation, an accurate LOFO estimation is necessary for subcarrier demultiplexing. As such, it is desirable to provide a solution for accurately estimating and compensating LOFO and chromatic dispersion for SS-SM signals.